Professor Thomas H. Parker

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Research Interests: My research is in geometric analysis and its connections with mathematical physics. This field involves intriguing combinations of ideas and techniques from several different fields, including algebraic geometry, differential geometry, topology, and partial differential equations. My recent work uses analytic methods to study Gromov-Witten invariants.

Current Teaching:   Math 868 Geometry & Topology                                                                Courses taught previous semesters
  

Other Information:   CV

My Ph.D. Students:
1994 Liviu Nicolaescu (Professor, Notre Dame University).
1996 Eleny-Nicoleta Ionel (Professor, Stanford University).
2001 Junho Lee (Associate Professor, Central Florida University).
2005 Jens Von Bergmann (MountainMath).
2011 Kwangho Choi (Lecturer, Dongguk University, Korea).
2014 Manousos Maridakis (Assistant Professor, Aristotle University of Thessaloniki, Greece).
2016 Ákos Nagy (Visiting Assistant Professor, U.C. Santa Barbara).
2021 Woongbae Park (Post-doctoral Associate, Syracuse University).
2023 Alan (Zhe) Zhang.

Current: Keshav Sutrave.

Honors
Fellow of the American Mathematical Society, 2013
Member, Institute for Advanced Study, Princeton, NJ, 2001-2002.
Frame Teaching Award, MSU Mathematics Department, 1998, 2014.
Phi Beta Kappa Teaching Award, Harvard University, 1982

Selected Publications

• Relating VFCs on thin compactifications (with E.-N. Ionel), Math Annalen, 375 (2019), 845-893.   pdf
• Thin compactifications and relative fundamental classes (with E.-N. Ionel), J. Symplectic Geometery, 17(3), 2019.
• The Gopakumar-Vafa formula for symplectic manifolds , Annals of Math., 187 (2018), 1-64 (with Eleny Ionel).
• A natural Gromov-Witten virtual fundamental class, (with E.-N. Ionel).
• Spin Hurwitz numbers and the Gromov-Witten invariants of Kahler Surfaces, (with Junho Lee). Comm. Analysis & Geometry, 21, No. 5, (2013).
• An obstruction bundle relating Gromov-Witten invariants of curves and Kahler Surfaces, Amer. J. of Math., 134 (2012), 453-506 (with Junho Lee).
• Geodesics and Approximate Heat Kernels.
• A Structure Theorem for the Gromov-Witten Invariants of Kahler Surfaces, J. Diff. Geometry, 77 (2007), 483-513 (with Junho Lee).
• Symplectic Gluing and Family Gromov-Witten Invariants, in Geometry and topology of manifolds, 147-172, Fields Inst. Commun., 47, AMS, 2005 (with Junho Lee).
• The Symplectic Sum Formula for Gromov-Witten Invariants, Annals of Math., 159 (2004), 935-1025 (with E.-N. Ionel).
• Corrigendum (with E.-N. Ionel) arxiv: 1510.06943.
• Relative Gromov-Witten Invariants, Annals of Math., 157 (2003), 1-52 (with E.-N. Ionel).
• What is a Bubble Tree?, Notices of the AMS 50 (2003), 666-667.
• Gromov Invariants and Symplectic Maps, Math. Annalen. 314 (1999), 127-158 (with E.-N. Ionel).
• Gromov-Witten Invariants of Symplectic Sums, Math. Research Letters 5 (1998), 563-576 (with E.-N. Ionel).
• The Gromov Invariants of Ruan-Tian and Taubes, Math. Research Letters 4 (1997), 521-532 (with E.-N. Ionel).
• Bubble Tree Convergence for Harmonic Maps, J. Diff. Geometry 44 (1996), 595-633.
• Pseudo-Holomorphic Maps and Bubble Trees, Jour. of Geometric Analysis, 3 (1993), 63-98 (with J. Wolfson).
• Non-Minimal Yang-Mills Fields and Dynamics, Invent. Math. 107 (1992), 397-420.
• A Morse Theory for Equivariant Yang-Mills, Duke Math. J. 66 (1992), 337-356.    Errata
• The Yamabe Problem, Bulletin of the AMS 17 (1987), 37-91 (with J. M. Lee).
• On Witten's Proof of the Positive Mass Theorem, Commun. Math. Phys. 84 (1982), 223-238 (with C. H. Taubes).
• Gauge Theory on Four-Dimensional Riemannian Manifolds, Commun. Math. Phys. 85 (1982), 563-602.

Mathematics Education Publications

Elementary Mathematics for Teachers (with S. Baldridge), Sefton-Ash Publishing, 2004.
Elementary Geometry for Teachers (with S. Baldridge), Sefton-Ash Publishing, 2008.

These two textbooks are designed for a year-long course on "Mathematics for Elementary (and Middle) School Teachers" taught in a mathematics department. Both are used in conjunction with actual elementary school texts --- the outstanding "Primary Mathematics" books from Singapore.The first book focuses on arithmetic; the second focuses on measurement and geometry, and includes probability and statistics. Available online here (but not on Amazon).

Instructor resources for the above two textbooks are freely available at this site.

A Study of Core-Plus Students Attending Michigan State University (with R. Hill). A study involving over 3000 Michigan students found that students arriving at Michigan State University from four high schools which began using the Core-Plus Mathematics program placed into, and enrolled in, increasingly lower level courses as the implementation progressed. The existence of a downward trend is statistically statistically very robust (p<.0001). The grades these students earned in their mathematics courses were also below average (p<.01). American Math. Monthly, 113 (2006), 905-921.